Check your understanding
36. Suppose we want to set up a triple integral over the
region defined by the inequalities x2 ≤ y ≤ 1 and
0 ≤ z ≤ 1 − y in the order dx dy dz. What are the
z limits?
(a) 0 ≤ z ≤ 1.
(b) 0 ≤ z ≤ 1 − y.
(c) 0 ≤ z ≤ 0.
(d) −∞ < z ≤ 1.
Answer: (a).
Explanation: We are given that 0 ≤ z ≤ 1 − y. Since
y ≥ x2, we must have y ≥ 0, so 1 − y ≤ 1. Note that (b)
does not make sense because y is not fixed. The answer
can only involve constants.